Related papers: Bell-CHSH inequality and unitary operators
We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We also present an example of unitary equivalence between shifts defined…
Relations between teleportation, Bell's inequalities and inseparability are investigated. It is shown that any mixed two spin-$1\over2$ state which violates the Bell-CHSH inequality is useful for teleportation. The result is extended to any…
The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…
A concise and self-contained introduction to the Bell inequality in relativistic Quantum Field Theory is presented. Taking the example of a real scalar massive field, the violation of the Bell inequality in the vacuum state and for causal…
The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…
We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are $N^2$ different binary measurements. These binary…
The Burchnall-Chaundy problem is classical in differential algebra, seeking to describe all commutative subalgebras of a ring of ordinary differential operators whose coefficients are functions in a given class. It received less attention…
Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint…
Entanglement is a critical resource used in many current quantum information schemes. As such entanglement has been extensively studied in two qubit systems and its entanglement nature has been exhibited by violations of the Bell…
An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum…
This work is concerned with extending the results of Calder\' on and Vaillancourt proving the boundedness of Weyl pseudo differential operators Op_h^{weyl} (F) in L^2(\R^n). We state conditions under which the norm of such operators has an…
We formulate the expectation value of the Bell-Zukowski operator acting on qubit states of a two-particle Bell experiment. By using the equivalence between a set of N copies of a two-qubit experiment and a standard two-setting Bell…
The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin 1/2 particles and photons,…
We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…
Inspired the low $\ell$ cosmic variance we present a study on the statistical variance expected in observing Bell's inequality violation by primordial quantum states violation. We consider the statistical variance inherent to three sets of…
We construct a wide class of bounded continuous variables observables that lead to violations of Bell inequalities for the EPR state and give an intuitive Wigner function explanation how to predetermine which operators won't ever exceed the…
The violation of Bell inequalities is often interpreted as showing that, if hidden variables exist, they must be contextual and non local. But they can also be explained questioning the probability space employed, or the validity of the…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We present an alternative definition of quantum entanglement for bipartite system based on Bell inequality and operators' noncommutativity. A state is said to be entangled, if the maximum of CHSH expectation value $F_{\max}$ is obtain by…